The structure-activity relationships (SAR) are investigated by means of the Electronic-Topological Method (ETM) followed by the Neural Networks application (ETM-NN) for a class of anti-cholinesterase inhibitors (AChE, 53 molecules) being pyridazine derivatives. AChE activities of the series were measured in IC50 units, and relative to the activity levels, the series was partitioned into classes of active and inactive compounds. Based on pharmacophores and anti-pharmacophores calculated by the ETM-software as sub-matrices containing important spatial and electronic characteristics, a system for the activity prognostication is developed. Input data for the ETM were taken as the results of conformational and quantum-mechanics calculations. To predict the activity, we used one of the most well known neural networks, namely, the feed-forward neural networks (FFNNs) trained with the back propagation algorithm. The supervised learning was performed using a variant of FFNN known as the Associative Neural Networks (ASNN). The result of the testing revealed that the high ETM's ability of predicting both activity and inactivity of potential AChE inhibitors. Analysis of HOMOs for the compounds containing Ph1 and APh1 has shown that atoms with the highest values of the atomic orbital coefficients are mainly those atoms that enter into the pharmacophores. Thus, the set of pharmacophores and antipharmacophores found as the result of this study forms a basis for a system of the anti-cholinesterase activity prediction.